Nonpolar singularities of local zeta functions in some smooth case

Joe Kamimoto, Toshihiro Nose

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

It is known that local zeta functions associated with real analytic functions can be analytically continued as meromorphic functions to the whole complex plane. In this paper, the case of specific (nonreal analytic) smooth functions is precisely investigated. Indeed, asymptotic limits of the respective local zeta functions at some singularities in one direction are explicitly computed. Surprisingly, it follows from these behaviors that these local zeta functions have singularities different from poles.

Original languageEnglish
Pages (from-to)661-676
Number of pages16
JournalTransactions of the American Mathematical Society
Volume372
Issue number1
DOIs
Publication statusPublished - Jan 1 2019

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Riemann zeta function
Singularity
Real Analytic Functions
Asymptotic Limit
Meromorphic Function
Smooth function
Argand diagram
Pole
Analytic function
Poles

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

Cite this

Nonpolar singularities of local zeta functions in some smooth case. / Kamimoto, Joe; Nose, Toshihiro.

In: Transactions of the American Mathematical Society, Vol. 372, No. 1, 01.01.2019, p. 661-676.

Research output: Contribution to journalArticle

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